Why is Standard Deviation based on L2 Variance and not L1 Variance
I've found the answer, the L2 is Standard Deviation, and the L1 is Mean Deviation. Standard deviation describes the variation better and the values are always different on different sets of X while the Mean Deviation gives the same values sometimes.


  *Footnote: Why square the differences? If we just add up the differences from the mean ... the negatives cancel the positives:
  
  standard deviation why a       (4 + 4 − 4 − 4) / 4  = 0 So that won't work.
  How about we use absolute values?
  
  standard deviation why a       (|4| + |4| + |−4| + |−4|) / 4  =  (4 + 4 + 4 +
  4) / 4 = 4 That looks good (and is the Mean Deviation), but what about
  this case:
  
  standard deviation why b       (|7| + |1| + |−6| + |−2|) / 4  =  (7 + 1 + 6 +
  2) / 4 = 4 Oh No! It also gives a value of 4, Even though the differences
  are more spread out.
  
  So let us try squaring each difference (and taking the square root at
  the end):
  
  standard deviation why a      √( (42 + 42 + 42 + 42) / 4 ) = √( 644) = 4
  standard deviation why b      √( (72 + 12 + 62 + 22) / 4 ) = √( 904) = 4.74...


Reference:
https://www.mathsisfun.com/data/standard-deviation.html